Problem: Express your answer as a mixed number simplified to lowest terms. $10\dfrac{2}{5}-6\dfrac{4}{8} = {?}$
Simplify each fraction. $= {10\dfrac{2}{5}} - {6\dfrac{1}{2}}$ Find a common denominator for the fractions: $= {10\dfrac{4}{10}}-{6\dfrac{5}{10}}$ Convert ${10\dfrac{4}{10}}$ to ${9 + \dfrac{10}{10} + \dfrac{4}{10}}$ So the problem becomes: ${9\dfrac{14}{10}}-{6\dfrac{5}{10}}$ Separate the whole numbers from the fractional parts: $= {9} + {\dfrac{14}{10}} - {6} - {\dfrac{5}{10}}$ Bring the whole numbers together and the fractions together: $= {9} - {6} + {\dfrac{14}{10}} - {\dfrac{5}{10}}$ Subtract the whole numbers: $=3 + {\dfrac{14}{10}} - {\dfrac{5}{10}}$ Subtract the fractions: $= 3+\dfrac{9}{10}$ Combine the whole and fractional parts into a mixed number: $= 3\dfrac{9}{10}$